The gradient of the tangent to a curve is the rate at which the curve is changing at a particular point. It is also known as the slope or the derivative of the curve at that point.
The gradient of the tangent to a curve can be calculated using the derivative formula, which involves finding the limit of the change in y over the change in x as the interval between two points on the curve approaches zero.
The gradient of the tangent to a curve represents the instantaneous rate of change of the curve at a specific point. It indicates the direction and steepness of the curve at that point.
The gradient of the tangent to a curve can give insight into the shape of the curve. A positive gradient indicates an upward slope, while a negative gradient indicates a downward slope. A larger gradient indicates a steeper slope, and a smaller gradient indicates a gentler slope.
The gradient of the tangent to a curve is important in science because it helps us understand how quantities are changing over time. It is used in many fields, including physics, engineering, and economics, to analyze and predict the behavior of various systems and phenomena.